-1. Finish CartesianProductEJA: add to_matrix(), random_instance(),...
- methods. I guess we should create a separate class hierarchy for
- Cartesian products of RationalBasisEJA? That way we get fast
- charpoly and random_instance() defined...
+1. Add cartesian products to random_eja().
2. Add references and start citing them.
-3. Implement the octonion simple EJA.
+3. Implement the octonion simple EJA. We don't actually need octonions
+ for this to work, only their real embedding (some 8x8 monstrosity).
4. Pre-cache charpoly for some small algebras?
5. Profile the construction of "large" matrix algebras (like the
15-dimensional QuaternionHermitianAlgebra(3)) to find out why
they're so slow.
+
+6. Instead of storing a basis multiplication matrix, just make
+ product_on_basis() a cached method and manually cache its
+ entries. The cython cached method lookup should be faster than a
+ python-based matrix lookup anyway.